<PRE><B>Question 698526</B>
&lt;br&gt;&lt;font face=&quot;Tahoma&quot;&gt;Carl is correct, he has cut the large piece into 2 equal smaller pieces.&lt;br&gt;

However, his explanation is not complete.&lt;br&gt;

What he drew was not only an angle bisector, but more importantly, a median!&lt;br&gt;

When you draw a median of a triangle, it does indeed cut the other side into 2 equal segments.&lt;br&gt;

Now, Carl has 2 small triangles.&lt;br&gt;

But are they congruent?  That is the question.&lt;br&gt;

Let&#39;s label our large triangle ABC, with A being the vertex with the 26 degree angle.&lt;br&gt;

Let&#39;s call the midpoint of the segment opposite vertex A, point D.&lt;br&gt;

Now, the 2 triangles that are formed are triangle ADB, and triangle ADC.&lt;br&gt;

Can we tell if these are congruent?  We can, here&#39;s how:&lt;br&gt;

AB is congruent to AC since it is an isoscoles triangle.&lt;br&gt;

BD is congruent to CD since D is the midpoint of BC.&lt;br&gt;

AD is congruent to itself by the reflexive property.&lt;br&gt;

Thus, triangle ADB is congruent to triangle ADC by the Side-Side-Side Theorem (SSS).&lt;br&gt;&lt;br&gt;

{{{drawing( 400, 400, -10, 10, -10, 10,
  
  triangle( 0, 5, -5, 0, 5, 0 ), 
  locate( 0, 5.7, A ), locate( -5, 0, B ), locate( 5, 0, C ), locate ( 0, 0, D ),

  red( line( 0, 5, 0, 0 ))
  )}}}
&lt;br&gt;&lt;br&gt;

I hope this helps!  Keep practicing!  :)&lt;br&gt;

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